Regular and Chaotic Dynamics

, Volume 21, Issue 7–8, pp 792–803 | Cite as

Regular and chaotic motions of a Chaplygin sleigh under periodic pulsed torque impacts

  • Alexey V. BorisovEmail author
  • Sergey P. Kuznetsov
Nonlinear Dynamics & Mobile Robotics


For a Chaplygin sleigh on a plane, which is a paradigmatic system of nonholonomic mechanics, we consider dynamics driven by periodic pulses of supplied torque depending on the instant spatial orientation of the sleigh. Additionally, we assume that a weak viscous force and moment affect the sleigh in time intervals between the pulses to provide sustained modes of the motion associated with attractors in the reduced three-dimensional phase space (velocity, angular velocity, rotation angle). The developed discrete version of the problem of the Chaplygin sleigh is an analog of the classical Chirikov map appropriate for the nonholonomic situation. We demonstrate numerically, discuss and classify dynamical regimes depending on the parameters, including regular motions and diffusive-like random walks associated, respectively, with regular and chaotic attractors in the reduced momentum dynamical equations.


Chaplygin sleigh nonholonomic mechanics attractor chaos bifurcation 

MSC2010 numbers

37J60 37C10 34D45 37E30 34C60 


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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Udmurt State UniversityIzhevskRussia
  2. 2.Moscow Institute of Physics and TechnologyDolgoprudnyiRussia

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